Finite Group Databasebeta

← #18010891

Subgroups — #18010891

Order 4736.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924597C212yesmaximal, complemented
2#14558443C212yesmaximal, complemented
3#14558441C212yesmaximal, complemented
4#14558104C211yesmaximal, characteristic
5C2×#10596957—22no—
6#11924597—22no—
7#11924597C2214yes—
8C22×Dic74C2211yescharacteristic
9#11924534C411yescharacteristic
10#11924534C2211yescharacteristic
11#11924523C411yescharacteristic
12#11924523C2211yescharacteristic
13#11924517—22no—
14#11924515—22no—
15#11924495C411yescharacteristic
16C2×#41×C37C411yescharacteristic
17#41×C37—42no—
18C2×Q8×C37C2×C411yescharacteristic
19C2×D4×C37—21no—
20C2×D4×C37C2×C411yescharacteristic
21C22×C4×C37—21no—
22C22×C4×C37C2×C411yescharacteristic
23C22×Dic37D412yes—
24C2×Dic74—42no—
25C2×Dic74C2×C411yescharacteristic
26C2×Dic74D412yes—
27C2×Dic74C2311yescharacteristic
28#10596957—24no—
29#10596957—42no—
30C2×#64438—42no—
31C22⋊Dic37—21no—
32C22⋊Dic37—22no—
33C22⋊Dic37—22no—
34C4⋊Dic37—21no—
35#10596936—22no—
36#10596936—22no—
37C4×Dic37C2×C411yescharacteristic
38C4×Dic37C2×C411yescharacteristic
39C23×C37—21no—
40C23×C37C22⋊C411yescharacteristic
41Q8×C37—41no—
42D4×C37—41no—
43D4×C37—42no—
44C2×C4×C37—22no—
45C2×C4×C37—21no—
46C2×C4×C37—42no—
47C2×C4×C37C22⋊C411yescharacteristic
48C2×C4×C37C22×C411yescharacteristic
49C2×Dic37—22no—
50C2×Dic37—22no—
51C2×Dic37—21no—
52C2×Dic37—21no—
53C2×Dic37C22⋊C412yes—
54C2×Dic37C2×D412yes—
55Dic74—41no—
56Dic74—42no—
57Dic74—41no—
58#64438—44no—
59C22×C37—41no—
60C22×C37—42no—
61C22×C37—41no—
62C22×C37#9912yes—
63C22×C37C2×C22⋊C411yescharacteristic
64C4×C37—21no—
65C4×C37—21no—
66C4×C37—41no—
67Dic37—22no—
68Dic37—22no—
69Dic37—41no—
70Dic37—41no—
71#2133—371nomaximal, Sylow
72C2×C37—21no—
73C2×C37—22no—
74C2×C37—81no—
75C2×C37C2×#9911yescharacteristic
76#536—371no—
77C2×#101—372no—
78#356—372no—
79#355—372no—
80C37#213311yescharacteristic, complemented, Sylow
81C2×#41#386611yescharacteristic
82C22×Q8—371no—
83C2×M16—742no—
84C4⋊Q8—371no—
85C4⋊Q8—371no—
86#124—371no—
87#124—371no—
88#123—742no—
89C22⋊Q8—742no—
90#117—371no—
91#101—374no—
92#101—742no—
93#41—42no—
94C2×Q8—372no—
95C2×Q8—371no—
96C2×Q8—371no—
97C2×Q8—1482no—
98C2×Q8C2×#386611yescharacteristic
99C2×D4—21no—
100C2×D4C2×#386611yescharacteristic
101C22×C4—21no—
102C22×C4—372no—
103C22×C4C2×#386611yescharacteristic
104M16—744no—
105M16—1482no—
106C2×C8—1482no—
107C4⋊C4—742no—
108C4⋊C4—742no—
109C4⋊C4—741no—
110C22⋊C4—742no—
111C22⋊C4—742no—
112C22⋊C4—741no—
113C42—371no—
114C42—371no—
115C23—21no—
116C23C22⋊#386611yescharacteristic
117Q8—41no—
118Q8—1482no—
119Q8—1481no—
120Q8—1481no—
121D4—41no—
122D4—42no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—42no—
126C2×C4—372no—
127C2×C4—372no—
128C2×C4—742no—
129C2×C4—742no—
130C2×C4—741no—
131C2×C4—741no—
132C2×C4C22⋊#386611yescharacteristic
133C2×C4C22×#386611yescharacteristic
134C8—1484no—
135C22—41no—
136C22—42no—
137C22—41no—
138C22#1192459412yes—
139C22C2×C22⋊#386611yescharacteristic
140C4—21no—
141C4—21no—
142C4—41no—
143C4—742no—
144C4—742no—
145C4—1481no—
146C4—1481no—
147C2—21no—
148C2—22no—
149C2—81no—
150C2C2×#1192459411yescharacteristic
subgroupG/H
centerC2C2×#11924594
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting, prime radicalC2×#41×C37C4
socleC2×C37C2×#99
cosocleC2×Dic74C23
hypercenterC2×#41#3866
hypocenterC37#2133
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11924597C2semidirect
2. #14558443C2semidirect
3. #14558441C2semidirect
80. C37#2133semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#119245972
#145584432
#145584412
#145581042
#213337